Oil and water ... Turner's Burning of the House of Lords and Commons. Photo: Philadelphia Museum of Art. On show in Tate Britain's Turner Whistler Monet exhibition

The Thames is the great London referent: metaphor and fact. Without the khaki, sediment-heavy river, our city would have no soul. Much of the original London, the riverside settlement, has been overbuilt, stacked, crammed, warped, twisted - until light is corkscrewed, bounced off dirty windows: a rare epiphany, a dole of pleasure. The memory is still present, of streets as sewers, floating sluggishly after rain; or, shocked by sunshine, baked into fissured mud. The surface of JMW Turner's massive oils, when you get close to them in their Tate Britain bunker, are a bouilla-baisse of steaming reds and yellows, stewed light, linseed and gristle. They duplicate the condition of a dried riverbed: a network of hairline cracks - like a vision, from the edge of the troposphere, of the Thames Estuary fracturing into a mantilla of tributaries.

Walking - within the Roman walls - we are aware of how London streets aspire to the condition of water. They solicit a re-connection with the Thames, the world ocean, the sources of trade and wealth. River gods in alcoves. Coade stone deities with fishy tails. Sir Edwin Cooper's old Port of London Authority building on Tower Hill is a Mount Olympus of decommissioned riverine emanations: body builders bulked-up like cosmological cartoons hoping to attract the attention of William Blake. Father Thames, in a chariot drawn by sea horses, oversees, with blind eyes, a city of greed, paranoia, self-aggrandisement. Traditions upheld, business as usual.

Fearful, we try to understand where we are, before we give ourselves up to the drift, the deceptive counter currents of the labyrinth. There are fleets of miniaturised vessels, blackened, carbonised, dressing the walls of financial institutions: fetishes of superstition. Even the dullest pedestrian, burdened with everyday panic and non-specific terror, will acknowledge the presence of underground rivers: Walbrook, Fleet. Liquid prompts guide our steps towards the scintillae of the supremely visible Thames.

Here begins the work of poets and painters, their argument and co-dependence; treacherous depths, imported narratives, shows of light. Here begins the difficulty with representing a force that resists representation. Here begins the substance out of which London's dreaming is made. The Thames floods, ebbs: a seductive surface, active, dirty, copywritten by Eliot, Pope, Spenser, Conrad, Céline.

When I worked, in the 1970s, as a gardener in Limehouse, I used to see the grey spectre, an X-ray with its own microclimate, of Francis Bacon. At the bus stop. Belted aluminium raincoat, hands in pockets. Solitary. He had a house in Narrow Street, convenient for social interaction, pub life, redundant dockers, but useless as a studio. He couldn't, he had no ambitions in that direction, paint the river. He kept the blinds down, promiscuous light was excluded. He couldn't paint at all; the shifts, the sounds, were overwhelming. He commuted to Kensington. The studio, in a noble tradition, was a down-river bolthole: off-limits, taking advantage of present malaise and a recoverable tradition of submersion and erasure.

Turner inherited property in Wapping, which included a pub, the Ship and Bladebone. He devoured river light and relished the potential profits that would accrue from Isambard Kingdom Brunel's Rotherhithe Tunnel. He enjoyed sexual favours hidden from the pinch of polite society. The Thames at Wapping reflected low skies, migrating weather systems. Turner worked, as always, inside and out, filling his sketchbooks: the heat of women's bodies, muscle and fold, twinned with meaty sunsets. A poker-red eye burning off the murk, the sullen damp. Locals knew the short, peppery gentleman as "Admiral Booth". He was often out on the river.

London air was foul, soot coating the lungs, but attractive to painters: a thick membrane penetrated by prismatic shafts. Turner was a walker. Like old Betty Higden in Dickens' last completed novel, Our Mutual Friend , he could manage 20 miles a day, if put to it. Even his ageing father, caretaker of the Twicken ham property, would trudge 11 miles, in and out of London, to open Turner's gallery. Painters shadow the river, struggling to fix the unfixable; trying to nail a fistful of mercury to a wet wall.

"I adore London," Monet said, "but what I love more than anything is the fog." Industrial pollution, sea coal fires, river fret: every element contributes to the London Particular. Light so thick you can taste it. Monet, a refugee from the Franco-Prussian war of 1870, factored strategic tourism into vision: unscripted postcard views dissolving sky into river. A grand project of dematerialisation. Visiting public places, Hyde Park, Green Park, the Embankment, he transfigured the dull weight of an imperial capital into reefs of pink coral, candy floss islands. Instantaneous sense impressions, graphs of mood temperature, were laboured over in the studio and reluctantly ceded to his dealer. The Thames below Westminster, painted in 1870, presents the new Houses of Parliament as a smoky cliff, a series of jagged outcrops. Monet established the franchise: Thames as melting Polaroid. Noise muffled, veiled in chiffon. Non-leisured citizens are deleted to enhance the calligraphic spasms.

Monet's friend and colleague, James McNeill Whistler (a man who was not-at-home everywhere), also progressed towards the elimination of vulgar riverside activity (human traces). He chose instead the pre-electronic virtuosity of "lamplight and starlight": medieval magic with a Japanese spin. Chelsea nocturnes, bruised minimalism: he had to deal with the nuisance of Crystal Palace on the southern horizon, an unsightly invasion of the actual. As much an affront to the elective decadence of the late 19th century as our own civic folly, the Millennium Dome on Greenwich Peninsula. Such is the characteristic Xerox impressionism of New Labour: a white blot, seagull droppings on a pristine computer screen. Whistler's zen bridges have been revamped as the portal to Thames Gateway.

Without the Thames, there would be no viable London aesthetic. What you depict will always overlap some previous account of the same view, a topographical record of the position from which the painting was made. The serial excursionism of Monet, with his privileged Savoy Hotel balcony, a room stacked with enough canvases to cover every freak of our infernal weather, interrogates contrary visions: upstream, downriver. Two bridges, two substantial chunks of civil engineering to be broken down into beads of shimmering light. London as a studio. Like Whistler, Monet took up Baudelaire's challenge: to depict "the landscape of great cities". The English Channel narrowed to a ditch, as poets and painters travelled in both directions. Sickert to Dieppe. Apollinaire to Lambeth. Stéphane Mallarmé translated Whistler's Ten O'Clock Lecture . Whistler and Monet made their treaty with the irritating genius of Turner; by studying his works, praising his energy, damning his failure to appreciate the subtle depths of shadow.

Riverside subjects are borrowed, never owned: the fireworks from the Cremorne pleasure gardens that decorate Whistler's Nocturne: Blue and Gold - Old Battersea Bridge (1872-5) return as flares in the wartime sky of Cecil Brown's A Prospect of London from the South East in the Year 1945. A wood engraving (skeleton rowing through drowned bodies), from Punch in 1858, is finessed into the opening sequence of Our Mutual Friend . Gaffer Hexam and his daughter corpse-fishing, setting up future television adaptations: London Gothic.

Images produced with such intense concentration become the medium by which folk memory survives: the thin, horizontal bands of Whistler's wet-on-wet technique in Nocturne: Blue and Silver - Chelsea (1871) are honoured in the recent work of that laureate of stagnant canals, filling stations and night football pitches, Jock McFadyen. McFadyen, in his large-scale representations of the silvery blight of Purfleet and the QEII Bridge, pays a very knowing homage. He follows his mentor into the aesthetics of entropy. They began, both of them, with peopled compositions, then let the actors go. McFadyen's dog walkers, his drinkers with half-cooked faces, occupy the riverside that Francis Bacon couldn't paint.

Where Monet worried at serial versions of the Houses of Parliament from a secure viewpoint in St Thomas' Hospital, the Scottish expressionist John Bellany goes a stage further: by moving in. For intrusive medical procedures, before a liver transplant in Cambridge. His river is yellow, vicious - like the anamorphic urban panoramas painted by Kokoshka from the upper floors of Millbank Tower. Monet shreds light into straw. Kokoshka butchers it, like a surgeon, to incubate an apocalypse of venture capital, bad news and worse politics.

So the business of colliding those blue-chip culture stocks - TurnerWhistlerMonet - for an exhibition at Tate Britain is not a harmless act. Complex issues of promotion, scholarship and sponsorship are involved. The show was first floated in 1988; at the time I was being fed sandwiches and coffee, while discussions were held on ways of making an event around the theme of the river. My unworkable (and definitively unfundable) proposal leant towards the Tate Gallery as a cabinet of dredged curiosities (after the fashion of John Tradescant's eccentric jumble, his Lambeth Ark). I wanted to retrieve the dark history of sugar, Sir Henry Tate's bequest shackled to the Silvertown refinery. I wanted documentation from the Tate's early disguise: as Millbank Penitentiary. And convalescent traces from the First War; the dying carried ashore, wheeled down a ramp into a subterranean chapel. I wanted to challenge the alternate art collection on the far shore, Lord Archer's penthouse conversation pieces. His Dufy riverscapes, his Monet totem like Winston Churchill's gifted trophy at Chartwell. (Owning a Monet is about owning a Monet, not seeing what it does or says.)

Art plunder, sanctified by public display, confers virtue on its keepers. A notable show diverts attention from the grubby realpolitik of the river. Tactfully hung apartments are what we require, walls with radiant windows. We file through, nudged by prompt cards, in money-laid-out reverence. While outside, en plein air, the Embankment is deserted. Sharky cruisers, defaced by a rash of expectorated Damien Hirst Smarties, shuttle between the ex-power station (Tate Modern) and the former prison (Tate Britain). The true exhibition, I decided, would involve knocking down that wall, letting the river in. Go with the flow. With Turner, dying in his Chelsea house, being absorbed in the rush of light; calling on his god, the sun.

· Turner Whistler Monet is at Tate Britain, London SW1, from Thursday to May 15. Tickets: 020-7887 8888 or www.tate.org.uk/tickets